My primary concern here is how FFA affects rank. If I understood correctly, only the winner gains rank progress in FFA games. Everyone else loses rank progress. In an ideally balanced teams or 1v1 game, chances of winning are 50%, so in the long term you would at least keep your rank. In an ideally balanced FFA game, assuming at least 3 players, it would be 33% at max. In reality it's even less as you usually have 4-6 players. So unless you are a really good FFA player, you can only lose rank in the long term when playing FFA games.
Another obvious reason is that players doing well in FFA might be doing bad in teams or 1v1 games in general. Same applies vice versa, a good teams player might do bad in FFA or 1v1. Or a good teams player doing bad in 1v1. Etc. This is why I think that Zero-K needs separate ranks based on game types.
I am also aware that this would result in a even more complicated ranking system. Open questions are how casual vs competitive would be handled and what rank would be displayed. In my opinion, the displayed rank would ideally be based on room type. Custom or bot/chicken rooms do not have to care about rank anyway.